4 ms·

This is my understanding too. I have a Kurzweil K2500 keyboard from around 1999 that has a bunch of the alternate tunings, including three from that era. The Ba

This is my understanding too. I have a Kurzweil K2500 keyboard from around 1999 that has a bunch of the alternate tunings, including three from that era. The Bach-era tunings weren't what we know of as "equal temperament." Truly equal temperament didn't come around until well after Beethoven was dead. I've always interpreted the "Well-Tempered" in Bach's title to mean that he was brining out the strength of each key. Some of those keys sound really "out of tune" to modern ears -- I have a friend with perfect pitch who legit can't listen to them. Owen Jorgensen's "Tuning the Historical Temperaments by Ear" is good bedtime reading on this topic, if you have a couple hundred bucks burning a hole in your pocket. https://www.amazon.com/Tuning-historical-temperaments-ear-eighty-nine/dp/091861600X https://www.amazon.com/Tuning-historical-temperaments-ear-ei...

wizofaus 4y ago
> Truly equal temperament didn't come around until well after Beethoven was dead Source for that? The concept and practice certainly existed well before Beethoven's time but it's less clear at which point it became the norm. Even the wikipedia article on 12 TET has "citation needed" for the claim that it happened in the early 19th century.
- joegahona 4y ago
  I don't remember where I learned this, but what you said is more accurate than what I said -- the concept was definitely known well before Beethoven, but my understanding is it wasn't the standard tuning on keyboard instruments until much later, and came to its fruition with all the atonal music of the early 20th century. I think composers even went so far as to assign emotions/moods to various keys based on each key's sound. E.g. "E-flat major is austere, D-minor is sad," etc. Might be worth reading: - https://books.google.com/books/about/The_Effects_of_Unequal_Temperament_on_Ch.html?id=O6b2tgAACAAJ https://books.google.com/books/about/The_Effects_of_Unequal_... - https://www.proquest.com/openview/b22142f819768ae82464aa2679f4ef68/1?pq-origsite=gscholar&cbl=18750&diss=y https://www.proquest.com/openview/b22142f819768ae82464aa2679...
  - tripa 4y ago
    More generally, I'd be curious to know how they'd practically tune a keyboard to 12TET before the electronic chromatic tuner got around. Start with Pythagorean fifths then compress ever-so slightly? How'd you keep them… equal?
    - hunter2_ 4y ago
      Oo I can take this one! I'm not a registered piano technician, but I've tuned my piano (and helped a few friends) for some 15 years. Aurally (as opposed to electronically) tuning a piano is actually pretty straightforward. I'll stop short of saying it's easy, but once you learn the method, it's very sensible and just a matter of practice. The general idea is to achieve consistent beat rates for a given interval -- major thirds being the most useful for its relatively high beat rate compared to other equally tempered intervals -- as you play it chromatically. By that I mean play A and C#, then Bb and D, then B and D#, etc. and if the beat rate hardly changes (but does consistently climb) then you've achieved equal temperament. Say you've got A tuned to a reference (tuning fork). Then set the A above that so there's no beating, since octaves are always perfectly 2:1 regardless of temperament (until the extremes, when you need to stretch a bit, but I digress). Then tune the C# and then tune the F. Basically it's an augmented triad, or a stack of three major thirds (including from F back up to A). Get all of them to beat by about the same amount, but the higher ones just slightly faster than the lower ones. The fact that this feat utilizes two A's is the key to pulling it off. You frame out the octave and then fill in the augmented triad. But now you need to do the next set: Bb, D, F#, Bb. How to get here without another external reference? Well, well, well. We have our ways. The perfect fourth between A and D is an option, but be careful not to make it actually a perfect integer (no beating), as that wouldn't be equal tempered; it should beat maybe about half as fast as the nearby major thirds, IIRC.
      - hunter2_ 4y ago
        Further reading: https://my.ptg.org/HigherLogic/System/DownloadDocumentFile.ashx?DocumentFileKey=1029971f-2eae-410f-9a14-dfd98216c51f https://my.ptg.org/HigherLogic/System/DownloadDocumentFile.a... Notably: > In equal temperament, all perfect fifths are “contracted”, while all perfect fourths as “expanded”. Minor thirds are contracted, while major sixths are expanded. Major thirds are expanded, while minor sixths are contracted. The piano tech must have knowledge of the approximate beat rates the intervals of equal temperament in the temperament octave: The beat rate of perfect fourths within the temperament octave may be about 1 beat per second. The beat rate of perfect fifths within the temperament octave may be about 1/2 beat per second. The beat rate of F3-A3 major third is about 7 beats per second and that of higher thirds are faster. In my previous comment, my memory was a bit off when I said "about half the beat rate"... that's the difference in rate between fourths and fifths, apparently. > Example: to check the tuning of D4 within the temperament octave, play A3-D4 and G3-D4. The fourth should beat faster than the fifth. If the fifth is too fast and the fourth too pure perhaps the D4 is flat; if the fourth and fifth beat at the same rate, perhaps the D4 is flat; if the fourth beats too fast and the fifth is too pure, perhaps the D4 is sharp. > you can use more and more checks as one progresses through the sequence and tune each new note as a “best compromise” with all the previous notes, that is, each new note will not depend only on the last note tuned, so there will be more of a chance that errors will not accumulate in the later notes tuned.

wizofaus 4y ago

> Truly equal temperament didn't come around until well after Beethoven was dead Source for that? The concept and practice certainly existed well before Beethoven's time but it's less clear at which point it became the norm. Even the wikipedia article on 12 TET has "citation needed" for the claim that it happened in the early 19th century.

joegahona 4y ago
I don't remember where I learned this, but what you said is more accurate than what I said -- the concept was definitely known well before Beethoven, but my understanding is it wasn't the standard tuning on keyboard instruments until much later, and came to its fruition with all the atonal music of the early 20th century. I think composers even went so far as to assign emotions/moods to various keys based on each key's sound. E.g. "E-flat major is austere, D-minor is sad," etc. Might be worth reading: - https://books.google.com/books/about/The_Effects_of_Unequal_Temperament_on_Ch.html?id=O6b2tgAACAAJ https://books.google.com/books/about/The_Effects_of_Unequal_... - https://www.proquest.com/openview/b22142f819768ae82464aa2679f4ef68/1?pq-origsite=gscholar&cbl=18750&diss=y https://www.proquest.com/openview/b22142f819768ae82464aa2679...
- tripa 4y ago
  More generally, I'd be curious to know how they'd practically tune a keyboard to 12TET before the electronic chromatic tuner got around. Start with Pythagorean fifths then compress ever-so slightly? How'd you keep them… equal?
  - hunter2_ 4y ago
    Oo I can take this one! I'm not a registered piano technician, but I've tuned my piano (and helped a few friends) for some 15 years. Aurally (as opposed to electronically) tuning a piano is actually pretty straightforward. I'll stop short of saying it's easy, but once you learn the method, it's very sensible and just a matter of practice. The general idea is to achieve consistent beat rates for a given interval -- major thirds being the most useful for its relatively high beat rate compared to other equally tempered intervals -- as you play it chromatically. By that I mean play A and C#, then Bb and D, then B and D#, etc. and if the beat rate hardly changes (but does consistently climb) then you've achieved equal temperament. Say you've got A tuned to a reference (tuning fork). Then set the A above that so there's no beating, since octaves are always perfectly 2:1 regardless of temperament (until the extremes, when you need to stretch a bit, but I digress). Then tune the C# and then tune the F. Basically it's an augmented triad, or a stack of three major thirds (including from F back up to A). Get all of them to beat by about the same amount, but the higher ones just slightly faster than the lower ones. The fact that this feat utilizes two A's is the key to pulling it off. You frame out the octave and then fill in the augmented triad. But now you need to do the next set: Bb, D, F#, Bb. How to get here without another external reference? Well, well, well. We have our ways. The perfect fourth between A and D is an option, but be careful not to make it actually a perfect integer (no beating), as that wouldn't be equal tempered; it should beat maybe about half as fast as the nearby major thirds, IIRC.
    - hunter2_ 4y ago
      Further reading: https://my.ptg.org/HigherLogic/System/DownloadDocumentFile.ashx?DocumentFileKey=1029971f-2eae-410f-9a14-dfd98216c51f https://my.ptg.org/HigherLogic/System/DownloadDocumentFile.a... Notably: > In equal temperament, all perfect fifths are “contracted”, while all perfect fourths as “expanded”. Minor thirds are contracted, while major sixths are expanded. Major thirds are expanded, while minor sixths are contracted. The piano tech must have knowledge of the approximate beat rates the intervals of equal temperament in the temperament octave: The beat rate of perfect fourths within the temperament octave may be about 1 beat per second. The beat rate of perfect fifths within the temperament octave may be about 1/2 beat per second. The beat rate of F3-A3 major third is about 7 beats per second and that of higher thirds are faster. In my previous comment, my memory was a bit off when I said "about half the beat rate"... that's the difference in rate between fourths and fifths, apparently. > Example: to check the tuning of D4 within the temperament octave, play A3-D4 and G3-D4. The fourth should beat faster than the fifth. If the fifth is too fast and the fourth too pure perhaps the D4 is flat; if the fourth and fifth beat at the same rate, perhaps the D4 is flat; if the fourth beats too fast and the fifth is too pure, perhaps the D4 is sharp. > you can use more and more checks as one progresses through the sequence and tune each new note as a “best compromise” with all the previous notes, that is, each new note will not depend only on the last note tuned, so there will be more of a chance that errors will not accumulate in the later notes tuned.